Question

Math

Posted 6 months ago

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One line passes through the points $(-8,1)$ and $(4,4)$. Another line passes through points $(-9,-7)$ and $(9,-3)$.
Are the lines parallel, perpendicular, or neither?
Choose 1 answer:
(A) Parallel
B) Perpendicular
(C) Neither
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To determine if the lines are parallel, perpendicular, or neither, we need to compare their slopes

step 2

The slope of the line through points $(-8,1)$ and $(4,4)$ is calculated as $\frac{4 - 1}{4 - (-8)} = \frac{3}{12} = \frac{1}{4}$

step 3

The slope of the line through points $(-9,-7)$ and $(9,-3)$ is calculated as $\frac{-3 - (-7)}{9 - (-9)} = \frac{4}{18} = \frac{2}{9}$

step 4

Since the slopes $\frac{1}{4}$ and $\frac{2}{9}$ are not equal, the lines are not parallel

step 5

To check for perpendicularity, we see if the slopes are negative reciprocals of each other. The negative reciprocal of $\frac{1}{4}$ is $-4$, which is not equal to $\frac{2}{9}$

step 6

Since the slopes are neither equal nor negative reciprocals of each other, the lines are neither parallel nor perpendicular

[1] Answer

(C) Neither

Key Concept

Slope comparison for parallelism and perpendicularity

Explanation

Two lines are parallel if they have the same slope and perpendicular if the product of their slopes is -1. In this case, the slopes are neither equal nor negative reciprocals, so the lines are neither parallel nor perpendicular.

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